Determining The Exact Value of

We want to determine the exact value of using known trig values. Note that

(In terms of degrees, we have noted that 15° = 60° - 45°). Then, from the sum formula for given above, we know that

It would be extremely difficult to find this exact value without the use of this difference formula. A problem similar to this one which would involve a sum formula would be to calculate the exact value of sin 75°.